Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
A method of resolution increase and noise removal in using shifrin-transform to measure particle size distribution Han yue2 Yang Zong-Ling1 Qiao Xing1 Qian peng3 Yuan Yin-Nan1 Ding Si-Hong1 Dai bing1,2* 1. School of Mechanical Engineering, Nantong University, Nantong, 226019, China; 2. School of Sciences, Nantong University, Nantong, 226019, China; 3.School of Geography, Nantong University, Nantong, 226019, China) Abstract: Based on laser diffraction and Shifrin-transform, the measurement method of particle size distribution has been improved extensively. While, in real measurements, some noise peaks exist in the data of inversion and are misread as particle distribution peaks. On the other hand, the improved method used a truncation function as a filter is hard to distinguish adjacent peaks. In this paper, by introducing bimodal resolution criterion, the filter function is optimized. And a quasi truncation function with the optimized filter function is studied to achieve optimal bimodal resolution and remove noise peaks. This new quasi truncation function fits multimode distribution very well. By combining the quasi truncation function with Shifrin-transform, noise peaks are removed well and the adjacent peaks are distinguished clearly. Finally, laser diffraction experiments are applied and the particle size distribution is analyzed by applying this method. The results show that the quasi truncation function has better bimodal resolution than the truncation function. Generally, by combining the quasi truncation function with Shifrin-transform, in particle size distribution measurements with laser diffraction, the bimodal resolution is greatly increased and the noise is removed well. And our results can restore perfectly the original distribution. Therefore, the new method by combining the quasi truncation function with Shifrin-transform provides a feasible and effective way to measure the multimode particle size distribution by laser diffraction. Key Words: diffraction; particle size distribution; Shifrin-transform; quasi truncation function; inversion; noise; resolution This research was financially supported by the National Science Foundation Funds of China (Grant No.51376095) and Jiangsu Province Environmental Research Projects (No.2014049). 1 In the measurement of particle size distribution (PSD), the optical method has been widely used I ( ) 0 because of its non-contact and quick testing J 12 ( x ) x 2 f ( x ) dx F 2 k 2 2 (1) particles testing techniques, represented by Coulter Where, k is the wave number, F is the focal length, is the scattering angle, and J 1 is the first counter and Malvern particle analyzer, respectively, level of the Bessel function of the first kind. And characteristics [1-7]. Single particle and group have been developed well. At the end of the last f x is the distribution function, as a function of century, due to the development of charge-coupled particle size. Chin and Shifrin [8,10,11] obtained the device (CCD) components, a method of PSD analytic solution of the inverse problem as measurement based on Shifrin-transform and laser n( x ) x 3 f ( x ) diffraction was also developed quickly [8-12]. This method has a high precision and the users don’t 2 xF 2 k 2 x J1 ( x )Y1 ( x ) 0 require knowledge of the information such as the d 3 [ I ( )]d d (2) distribution model in advance [7,8,10,11]. However, it has a significant defect [8,9,11,12]. That is, in actual Where, n x is the distribution of particle quality measurements, noise in the data of inversion can as a function of size, and Y1 is the first level of the easily be misread as PSD peaks, which blocks it Bessel function of the second kind. Equation (2) is applying widely. Recently,we proposed a filter that called Shifrin-transform, which can invert the PSD involved inserting a truncation function to avoid using the angle distribution of the light scattering misreading noise peaks [12]. However, in our recent intensity. experiments, the bimodal resolution was low because Many previous reports [6,10-12] have showed that of the adjacent peak overlap effect. In order to remove the actual range of sampling angles needs to be the noise peaks and increase its bimodal resolution, a from min to max in equation (2) . So, data loss is quasi truncation function, with an optimized filter inevitable in actual sampling. This loss of data brings function is proposed in this paper to increase the some noise, which can be easily misread as bimodal resolution. And then the quasi truncation distribution peaks. In fact, this phenomenon makes function is combined with Shifrin-transform to solve shifrin method become a fatal flaw in the extended the problem of noise and adjacent peak overlap. This application quickly. After that, Dai Bing et al. [12] method specifies an effective way for using proposed a complete truncation function (CTF) based Shifrin-transform and laser diffraction to obtain on some characteristics of Fourier transform to multimode PSD. improve Shifrin method. The filter function was defined as 1. Shortcoming of Shifrin-transform inversion and CTF method Particle size parameter is set to x ( x d , is the wavelength of incident light, and d is the particle diameter), and x 1 . For a large number of particles, if the optical thickness is far less than 1, A( ) (1 ( 3/2 3/2 ) ) max (3) In some experimental measurements [12], the method can remove noise, perfect to restore the original distribution. While, when two of the peaks are then only single scattering can be considered. In fact, closed, serious problems will be encountered. Fig.1 single scattering is appropriate assumptions for shows the simulation inversion of PSD with three practical peaks using CTF and Shifrin method respectively. problems encountered in real time diffraction Here, n x is the ratio of the particle quality with approximation, the total scattering intensity on the size parameter x and the total particle quality with all focal plane of the objective lens is described as sizes (the same as below), and defined as a positive [10,11,13] value according to its physics significance (the same [1,3,10,11]. According to the 2 as below). In its original distribution, particle sizes at In order to obtain the optimal filter function, based three peaks are 25.0µm, 32.0µm, and 50.0µm, on the influence of filter function on the noises and the respectively, and the sampling angles are assumed to peak be within a range of 0.1 to 5.0 (seen also in Fig.2 and Fig.3). Due to the data collecting difficultly performance of filter function, a quasi truncation below 0.1 , the minimum of the sampling angle is peak resolution than the complete truncation function selected as 0.1 , and, due to the approximate requirements of Fraunhofer diffraction, the maximum and the other filter function. The quasi truncation Especially, the noise peak at 42µm is easily misread as distribution peak. For CTF method, the noises in closed peaks become indistinguishable in CTF method. It is fatal for restoring the original distribution. the min A( ) 1 [ ] ( max min ) 1 1 =1.15, = + , 2 2 Shifrin method are much larger than the CTF method. the original distribution, overlap seriously. These two adjusting truncation function (QCTF) is selected as follows Fig.1, it is observed that the noises in inversion for problem that the two peaks, at 25.0µm and 32.0µm in by function is found out, which has a better neighbor of the sampling angle is selected as 5.0 . Seen from inversion nearly disappear. But it causes another resolution, (4) In order to explain the peak resolution problem, here, a bimodal distinguish criterion, learning from the light wave resolution method in wave optics [14,15], is introduced here. When the distance ( ) of two peak positions is half of the sum (L) of full-width at half maximum of each peak, the two peaks can be CTF method 2 can be L bimodal resolution, appropriately distinguished. Therefore, shfrin method used to represent the 2 2 1 , two peaks can’t be 2 . When L L 2 1 , two peaks can be distinguished. When L 2 1 , two peaks appropriately distinguished. When L n(x) and 0 0 20 40 d/m 60 80 100 can be distinguished well. The larger is Fig.1 Simulation inversion of PSD with three peaks using CTF and shifrin methods. Particle sizes of peaks are 25.0µm, 32.0µm and 50.0µm respectively. 2 , the higher L is the bimodal resolution. Fig.2 is the simulation inversion of PSD with five peaks using shifrin method, CTF method and QCTF method. Peak particle sizes are 20.0µm, 26.5µm, 2. Proposal of a new method 40.0µm, 47.0µm, and 65.0µm respectively. Seen from In order to restore the original distribution well, the result of measurement needs to be small noise, high resolution, and high accuracy. Reported works [8-12] have pointed out Shifrin method has high measurement precision. But it has also serious noises. While CTF method has low noised, but low neighbor peak resolution. Therefore, an optimal filter function or the other methods to meet the requirements of both the noise removal and high resolution are found out in Fig.2, and according to our bimodal resolution criteria, the neighbor peaks at 20.0µm and 26.5µm, as well the ones at 40.0µm and 47.0µm, cannot be distinguished for the CTF method, while, for the QCTF method, they can be distinguished. Thus, the QCTF method has higher bimodal resolution than the CTF method. At the same time, the QCTF method, as well as the CTF method, has better noise removal than the Shifrin method, as shown in Fig.2. the following section. 2.1 A quasi truncation function 3 QCTF method CTF method shfrin method 15.0µm, 23.0µm, 45.0µm, 51.5µm, 70.0µm, 75.0µm. According to the QCTF inversion results, the new method is redistricted in the interval of 0.0µm-100.0µm. And shifrin method is applied for three intervals of 12.0µm-25.0µm, 42.0µm-53.0µm, n(x) and 68.0µm -78.0µm. The QCTF method is applied for the other intervals. current method QCTF method CTF method 20 40 d/m 60 80 100 Fig.2 Simulation inversion of PSD with five peaks n(x) 0 using QCTF, CTF and shifrin method. Peak particle sizes are respectively 20.0µm, 26.5µm, 40.0µm, 47.0µm and 65.0µm. A lot of simulation experiments have indicated that QCTF method has high bimodal resolution, and it is 0 20 40 d/m 60 80 100 suitable to simulate single, bimodal and multimodal Fig.3 Simulation inversion of PSD with six peaks particle distribution. However, QCTF method can using CTF method, QCTF method and our current reluctantly distinguish the two peaks at 20.0µm and method. Peak particle sizes are 15.0µm, 23.0µm, 26.5µm in Fig.2. That is to say, on the basis of noise 45.0µm, 51.5µm, 70.0µm and 75.0µm, respectively. removal, even the optimal filter function method is difficult to solve fundamentally the adjacent peak Seen from Fig.3, although the CTF method can overlapping problem. The original reason is that, remove noises, it is almost unable to restore the besides the characteristics of the noise removal, the original PSD because of the adjacent peak overlap optimal filter function method stretches the peak effect. Two peaks at 45.0µm and 51.5µm, as well as width, which declines the bimodal resolution. the ones at 70.0µm and 75.0µm, cannot be 2.2 The method of combination quasi truncation distinguished. On the other hand, the bimodal function with Shifrin-transform resolution of the QCTF method is better the results of Seen from Fig.1 and 2, Shifrin method has narrower the CTF method, while the two peaks at 70.0µm and peak width than the others. Then, a method of 75.0µm still cannot be distinguished. The method of combination the quasi truncation function with combination the QCTF and Shifrin-transform greatly Shifrin-transform is proposed here to obtain better increases the bimodal resolution. Seen from Fig.3, it noise removal and narrower peak width. Firstly, shows clearly that the six PSD peaks are separated QCTF method is applied to do the inversion. Then the well and, there has been almost no noise on the curve. inversion interval is redistricted according to the Thus, the current method combining the QCTF and inversion results. After that, Shifrin method is applied Shifrin-transform can perfectly solve both the noise for those intervals with particle distribution peaks, and obstacle and adjacent peak overlap effect. QCTF method is applied for the other intervals. Fig.3 shows the simulation inversion of PSD with six peaks 3. Experimental verification using CTF method, QCTF method and our current method. The peak particle sizes are respectively 3.1 Equipment and method of experiment 4 As shown in Fig.4, the optical particle-sizing measured by various techniques for the mixture of instrument used in our study is mainly composed of a GBW(E) 120006, GBW(E) 120042, GBW(E) 120045 He-Ne laser, an attenuation system, an extended and GBW(E) 120046. Here, the laser wavelength is filtering collimation system, a sample box, a lens, a 632.8 nm, the focal length of the objective lens was wedge-shaped baffle, a line array CCD, a probe circuit, 300 mm. Then, the angle interval can be calculated a data acquisition card, and a computer system. The standard particle latex spheres were provided by the as 11 m / 300mm 0.002101 . And the sampling angle min and max are 0.3004 and 4.7941 , Nuclear Industry Beijing Institute of Chemical respectively, and the total number of pixels is 2140. Engineering. Mean value of three tests was taken as the light 6 intensity distribution result. When the current method was used to measure PSD with three peaks, according to the results of QCTF method, Shifrin method was 1 applied for 17.0µm-30.0µm and 42.0µm-48.0µm 3 2 4 7 5 intervals, and QCTF method was applied for the other intervals. When PSD with four peaks was measured, comp- data probe Shifrin method was applied for 17.0µm-30.0µm and uter card circuit 42.0µm-53.0µm intervals, and QCTF method was applied for the other intervals. 1-Laser 2- Attenuator 3-Extender filter 4-Sample Seen from Fig.5 and Fig.6, results of Shifrin 5- Lense 6- Wedge baffle 7-CCD method bring many noise peaks, while results of CTF Fig. 4 Schematic of the optical particle-sizing method result serious adjacent peak overlap effect. instrument Therefore, they cannot restore their original PSD. The particles labeled GBW(E) 120006 (nominal Results of QCTF method do not only remove the peak size is 20.46±0.4µm), GBW(E) 120042 (nominal noises, but also have certain bimodal resolution. The peak size is 27.10±1.3µm) and GBW(E) 120045 neighbor peaks formed by GBW(E) 120006 and (nominal peak size is 45.60±1.3µm) were suspended GBW(E) 120042 are separated by QCTF method in pure water, and then the mixture of PSD with three (seen in Fig.5 and Fig.6). While the adjacent peaks peaks was formed. The particles labeled GBW(E) formed by GBW(E) 120045 and GBW(E) 120046 are 120046 (nominal peak size is 51.20±0.6µm) were not distinguished by QCTF method (seen in Fig.6). On dropped into the above suspension, and then the the other hand, the method of combination the QCTF mixture of PSD with four peaks was formed. By with Shifrin-transform can clearly show all peaks of adjusting the attenuation system, the scattered light the original distribution on the basis of noise removal. intensity distribution on the CCD was properly As shown in Fig.5, and Fig.6, peak particle sizes are obtained, and the obtained signal was converted to an measured to be 20.3µm, 27.4µm, 45.7µm, and 51.5µm, electric signal. The model of the Linear CCD was respectively, which are agreement with the nominal TCD103C (Toshiba) with 2592 pixels and the size of a sizes of the samples. Hence, as analyzed from above pixel was11.0µm. In order to reduce the influence of results, the current method has not only high bimodal the central spot, it was blocked by a wedge-shaped resolution but also good effect of the noise removal. baffle. The 3.2 Results and analysis of experiment Shifrin-transform can be applied widely to measure Fig.5 is the results of PSD measured by various method of combination the QCTF with the PSD of group particles by laser diffraction. techniques, including the current method, QCTF method, CTF method, and Shifrin method, for the mixture of GBW(E) 120006, GBW(E) 120042, and GBW(E) 120045. And fig.6 is the results of PSD 5 current method QCTF method CTF method restore the original PSD. (c).The current method fundamentally improves the inversion method based on Shifrin-transform, and it provides a feasible and effective way for measuring shifrin method n(x) actual PSD by laser diffraction. Acknowledgement This research was financially supported by the National Science Foundation Funds of China (Grant No.51376095) and Jiangsu Province Environmental Research Projects (No.2014049). We gratefully acknowledge the help of Prof. Xiangdong Luo, who 0 20 40 d/m 60 80 100 give a lot of advisers in our work and English polishing. Fig.5 PSD obtained by various techniques for mixture of GBW(E)120006, GBW(E)120042 and Corresponding author GBW(E)120045 Dai Bing, email:[email protected] current method QCTF method CTF method shifrin method References: [1] Zhang Z W, Zhen G, Yu X H, et al. A Novel Laser Size Analyzer within Fraunhofer Diffraction n(x) Used to Measure Intermittent Sprays [J]. CHINESE JOURNAL OF LASERS, 1995, 22(10):743-746. [2] Carter R M, Yan Y, Lee P. On-line nonintrusive measurement of particle size distribution through digital imaging [J]. IEEE Transactions on instrumentation and measurement, 2006, 55(6): 0 20 40 d/m 60 80 100 2034-2038. [3] Lei G, Shao K R, Li Y B, et al. Bayesian Fig.6 PSD obtained by various techniques for mixture Inversion of GBW(E)120006, GBW(E)120042, GBW(E)120045 Determination for the Estimation of Particle Size and GBW(E)120046 Distribution in Ferrofluids [J]. IEEE Transactions Method and its Information on magnetics, 2009, 45(10):3981-3988. 4. Conclusion [4] Mroczka J, Szczuczyński D. Simulation research (a). The method of quasi truncation function has good on improved regularized solution of the inverse bimodal resolution on the basis of noise removal, and problem in spectral extinction measurements [J]. it is an optimal selection to directly invert PSD by the Appl. Opt., 2012, 51(11):1715–23. analytic method. However, bimodal resolution is [5] Tang H, Liang G W. Inversion of particle size limited by stretched peak width characteristic of the distribution from spectral extinction data using the quasi truncation function. (b). A method of combination quasi truncation bimodal Johnson's SB function [J]. Powder function with Shifrin-transform is proposed. This [6] Heekyu Choia, Woong Leea, Seongsoo Kimb,et method not only has good effect of noise removal but al. Optimum refractive index of poly-component Technology, 2010 (198): 330–336. also high bimodal resolution, and is favorable to 6 particulate systems for measurement of particle shifrin size distribution by laser diffraction method Engineering, 1994, 116:357-362. analyzer [J]. Materials Chemistry and Physics, 2009(117):18–22. for aerosol particle size distribution using SPSO associated with multi-lognormal [J]. Journal of Fluids [11] Zhou W, Cao W X, Sun Z H. Theoretical Analysis on [7] Yuan Y Y, Hong L, Shuai Y, et al. Inverse problem inversion Measuring Particle-size Distribution by Shifrin-transform [J]. The Journal of Light Scattering, 2007, 19 (3): 236-241. distribution [12] Dai B, Yuan Y N, Bao Z H, et al. An Improved model [J]. Atmospheric Environment, 2011, Method for Inversion of Particle Size Distribution 45(28): 4892-4897. from Scattering Spectrum [J]. Spectroscopy and [8] Dai B, Bao Z H, He A Z. Research on A New Technique of Laser Diffraction for Measuring Particle-size Distribution[J]. Journal of Optoelectronics & laser, 2002, 13 (6):599-602. and Classification of Particle Size Distribution Dependent Model Algorithm [13] Dai B, Luo X D. Multiple light scattering of non-spherical particles with elliptical cross section [J]. [9] Sun X G, Tang H, Yan G B. Study of Inversion under Spectral Analysis, 2011, 31 (2):539-542. [J]. Spectroscopy and Spectral Analysis, 2008, 28(5): 1111-1114. ACTA PHYSICA SINICA, 2009, 58(6):3864-3868. [14]A. K. Ghatak, K. Thyagarajan.contemporary optics [M], plenum press, 1978. [15]Cheng Shou-zhu, Jiang Zhi-yong. Physics [M], higher education press, 1998. [10] Albert R, Farrell P V. Droplet sizing using the 在 Shifrin 变换测量粒度分布中 同时提高分辨率及去除噪声的方法研究 韩月 2 杨宗苓 1 乔星 1 钱鹏 3 袁银男 1 丁思红 1 戴兵 1,2 (1. 南通大学 机械工程学院,江苏 南通 226019;2.南通大学 理学院,江苏 南通 226019; 3. 南通大学 地理科学学院,江苏 南通 226019) 摘 要: 基于激光衍射和 Shifrin 变换测量颗粒尺寸分布的方法已经得到进一步改进,然而在 实际测量时,反演数据中存在一些易被误读为分布峰的噪声,另一方面,已有的以完全截断 函数为滤波函数的改进方法又存在不易分辨邻近双峰的缺陷。为此,文章引入双峰判据并优 化滤波函数,提出一种准截断函数,实现最优的双峰分辨率及去噪的目的,且能适应多种模 式的分布。通过将准截断函数与 Shifrin 变换相结合,既很好地去除噪声又使邻近峰可辩。最 后应用该法通过激光衍射实验对粒度分布进行了验证测量。结果表明:准截断函数方法较完 全截断函数方法的双峰分辨率有所提高,而将准截断函数与 Shifrin 变换相结合,可大大提高 双峰分辨率,并去除噪声,完美还原原分布。因此,该法为利用激光衍射反演测量多模式的 粒度分布提供了一条可行及有效的途径。 关键词:衍射;颗粒粒度;测量;Shifrin 变换;准截断函数;反演;噪声;分辨率 基金项目:国家自然科学基金资助项目,基金号:51376095。江苏省环保科研课题,项目号:2014049 作者简介:韩月(1990-),女,硕士研究生,从事颗粒的激光测试技术研究。 导师简介:戴兵(1964-),男,教授,从事颗粒的散射理论及测试技术研究。[email protected] 通讯联系人:戴兵,Email: [email protected] 7